Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def binarySearch(arr, l, r, x): 
    while l <= r: 
        mid = l + (r - l)//2; 
        if arr[mid] == x: 
            return mid 
        elif arr[mid] < x: 
            l = mid + 1
        else: 
            r = mid - 1
    return -1
  
n = int(input())
ll = []
for k in range(1, 47722):
    ll.append(int((k*(k+1))//2))
found = False    
for k in (ll):
    j = n-k
    pos = binarySearch(ll, 0, len(ll)-1, j)
    if pos >= 0:
        found = True
        break

if found:
    print("YES")
else:
    print("NO")